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Different versions of the Compound Interest Formula. The general formula is: T = P(1 + I/n)Yn where: T = Total amount of money P = Principle amount of money I = Interest as a decimal. n = How often interest is calculated in a year. Y= Number of years. This formula can be used to calculate the total amount of money a single investment will be worth if values for P, I, n and Y are given. What if we wanted to find P instead? There are several practice problems that ask you to find P. The best way to tackle these problems would be to solve T = P(1 + I/n)Yn for P and use that formula for those problems. Here is how we get that formula. I T P1 n Yn We want P alone and what we have is P times another number so divide. Yn T I 1 n So, P Yn I P1 n Yn I 1 n T I 1 n Yn We can use this formula to find P if we are given T, I, n and Y. We can also use this formula to find I. This is a little tougher and it involves a technique that hasn’t been fully explored in this course. I T P1 n Yn We want to get I alone but it is inside the group that has the exponent Yn. We can move the P by dividing. Yn I P 1 Yn T T I n We now have 1 P n P P We need to do something about the exponent. Let’s use a simpler equation to demonstrate the method to be used. Find the exponent that makes the following equation a true statement. (34)x = 3 First, let’s review one of the rules of exponents that was introduced in Module 3. Multiply the exponents: (34)5 = 345 = 320 Therefore, (34)x = 34x and 34x = 3 = 31 To find x we can solve the equation: 4x = 1 Thus x = ¼ and (34)1/4 = 3. Yn T I 1 . To get the variable I P n out of the group we need the exponent to be 1. This can be done be the exponent 1/Yn to both sides of the equation. How do we use this? Well, we have the equation 1 Yn 1 1 Yn I Yn I T T Yn 1 which simplifies to 1 . We’re now two steps from n P P n the formula we’re looking for. 1 I T Yn 1 11 n P 1 I T Yn 1 n P 1 T Yn I n 1 n P n 1 T Yn Thus , I n 1 P We can use this formula to find I if we are given T, P, n and Y. The formula to find Y is developed in Unit 4 of this Module 8. Here are all the formulas that are related to calculating Compound Interest. T P1 I n Yn is used when P, I, n and Y are given. 1 T Yn I n 1 is used when T, P, Y and n are given. P P T I 1 n Yn is used when T, I, n and Y are given. T log P Y is used when T, P, I and n are given. I n log 1 n These formulas are used to solve the practice problems for Units 2 and 4.